From a866d7cd6672474e9376617aadc91424b9ba3506 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Sun, 8 May 2022 22:37:45 +0200
Subject: add Fresnel presentation

---
 vorlesungen/slides/fresnel/integrale.tex | 72 ++++++++++++++++++++++++++++++++
 1 file changed, 72 insertions(+)
 create mode 100644 vorlesungen/slides/fresnel/integrale.tex

(limited to 'vorlesungen/slides/fresnel/integrale.tex')

diff --git a/vorlesungen/slides/fresnel/integrale.tex b/vorlesungen/slides/fresnel/integrale.tex
new file mode 100644
index 0000000..7798932
--- /dev/null
+++ b/vorlesungen/slides/fresnel/integrale.tex
@@ -0,0 +1,72 @@
+%
+% fresnel.tex -- slide template
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\input{../slides/fresnel/eulerpath.tex}
+\begin{frame}[t]
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\frametitle{Fresnel-Integrale}
+\vspace{-20pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.48\textwidth}
+\begin{block}{Definition}
+Fresnel-Integrale:
+\begin{align*}
+S(t)
+&=
+\int_0^t \sin(\tau^2)\,d\tau
+\\
+C(t)
+&=
+\int_0^t \cos(\tau^2)\,d\tau
+\end{align*}
+\uncover<2->{%
+Können nicht in geschlossener Form ausgewertet werden.
+}
+\end{block}
+\uncover<3->{%
+\begin{block}{Kurve}
+\[
+\gamma(t)
+=
+\begin{pmatrix}
+S(t)\\C(t)
+\end{pmatrix}
+\]
+\end{block}}
+\end{column}
+\begin{column}{0.48\textwidth}
+\uncover<4->{%
+\begin{block}{Euler-Spirale}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick,scale=2.7]
+
+\draw[->] (-1.05,0) -- (1.05,0) coordinate[label={$C(t)$}];
+\draw[->] (0,-1.05) -- (0,1.05) coordinate[label={right:$S(t)$}];
+
+\draw[color=red,line width=1.4pt] \fresnela;
+\draw[color=red,line width=1.4pt] \fresnelb;
+
+\fill[color=blue] ({sqrt(3.14159/8)},{sqrt(3.14159/8)}) circle[radius=0.02];
+\fill[color=blue] ({-sqrt(3.14159/8)},{-sqrt(3.14159/8)}) circle[radius=0.02];
+
+\draw (1,-0.03) -- (1,0.03);
+\node at (1,-0.03) [below] {$1$};
+\draw (-1,-0.03) -- (-1,0.03);
+\node at (-1,0.03) [above] {$-1$};
+\draw (-0.03,1) -- (0.03,1);
+\node at (-0.03,1) [left] {$1$};
+\draw (-0.03,-1) -- (0.03,-1);
+\node at (0.03,-1) [right] {$-1$};
+\node at (0,0) [below right] {$0$};
+
+\end{tikzpicture}
+\end{center}
+\end{block}}
+\end{column}
+\end{columns}
+\end{frame}
+\egroup
-- 
cgit v1.2.1

